Answer
Since $\frac{5\pi}{6} \gt \frac{\pi}{2}$, then $arcsin(sin~\frac{5\pi}{6}) \neq \frac{5\pi}{6}$
Work Step by Step
$arcsin(sin~\frac{5\pi}{6}) = arcsin(0.5) = \frac{\pi}{6}$
The domain of arcsin is $[-\frac{\pi}{2}, \frac{\pi}{2}]$
Since $\frac{5\pi}{6} \gt \frac{\pi}{2}$, then $arcsin(sin~\frac{5\pi}{6}) \neq \frac{5\pi}{6}$
